a·b equals the length of a times the projection of b onto a's direction, and its sign tells you whether the angle is acute or obtuse.
Module goal. Introduce the operation that multiplies two vectors into a number, capturing the angle between them, projection, and when they're perpendicular.
eastmath.com · 27.4 The Dot Product: Angles and Perpendicularity · 27.4.3 What the Dot Product Means Geometrically